Cyclic evaluation of energy-dissipating hysteretic infilled reinforced concrete frame: A novel approach as low-cost passive energy

Abstract

A novel energy-dissipating hysteretic infilled wall system comprising slotted concrete blocks with energy-dissipating links is designed and experimentally tested in a full-scale reinforced concrete frame. Its performance is compared with the conventional (brick) infilled frame as well as bare frame. This infill wall system helps to reduce the stiffening effect and also acts as a secondary load-resisting system that resists lateral loads even after the formation of plastic hinges in the frame. The post-yield response of the frame becomes stable and no collapse condition arises even at a large deformation. This is a kind of low-cost passive energy–dissipating method that may act as an efficient and versatile solution to minimize the damages in frame buildings. A systematic numerical model is developed on the basis of a series of experiments conducted on its constituent units that captures the elastic and post-yield load deformation behavior of the energy-dissipating hysteretic infilled frame under cyclic loading.

Keywords

Energy-dissipating hysteretic infill low-cost passive energy dissipator infilled RC frame inelastic behavior friction energy-dissipating links

Introduction

The past studies conducted on the conventional stiffened infill wall system show that it significantly and spontaneously increases the stiffness of the infilled frame during a severe earthquake that may cause brittle shear failure particularly in the non-ductile frames of the building. Vulnerability of such construction is exposed after collapse or extensive damages in the recent earthquakes (De la Llera et al., 2017; De Luca et al., 2014; Gautam et al., 2016; Yataǧan, 2011). Sometimes, the pre-peak behavior of the conventional infill walls that initially seems to be advantageous, actually becomes the root cause of brittle shear failure of the frame members and subsequently post-peak or post-yield strength of the frame falls abruptly causing sudden collapse and loss in residual capacity (Dolšek and Fajfar, 2004; Paulay and Priestley, 1992). In this research, efforts are made to replace the conventional stiffened infill wall system with energy-dissipating hysteretic (EDH) infill wall system that not only arrests the diagonal strut action but also provides a stable post-yield behavior and ductile failure mechanism.

In this study, a new and affordable technique of interlinked concrete blocks with energy-dissipating links (EDLs) as infill in reinforced concrete (RC) frame is conceptualized and designed to exploit the frictional and elastomeric damping present in the system. Frictional damping arises between the rigid surfaces of the blocks in contact, which slides one over the other while the elastomeric damping arises from the straining of EDLs that restrict the translational and rotational movement of each block. The sliding friction can be effectively used as a damping mechanism for the dissipation of energy and sometimes may be very effective since it offers uniform dissipation across the entire frequency range. It is not only an effective and cost-efficient system, but also an easy-to-implement strategy for earthquake-resistant building construction. However, the construction of EDH infill wall requires precise workmanship and prior provision for its installation in the RC frames.

Concept of EDH infill wall system

The concept of EDH infill wall system consists of slotted concrete blocks (may be other industrial waste such as fly ash, silica flume, etc.) along with EDLs (made up of “ply” part of used radial rubber tire, a co-polymer of Styrene–butadiene rubber laminated with very thin steel plates). These blocks are capable of small translations and rotations allowing the infill to mimic the deformation of the frame in flexural mode. There are two main sources of energy dissipation in the EDH infill wall system, namely friction along different layers of the blocks and yielding of the EDLs. The aim of providing the EDH infill wall system is to develop an additional energy-dissipating system that resists the lateral load and simultaneously helps in reducing the damage in the structural members of the frame, Figure 1. Moreover, the large-scale production of the required slotted blocks and EDLs manufactured from used rubber tires has the potential to generate new employment; promote micro, small, and medium enterprises (MSMEs); and waste management.

Experimental program

Hysteresis behavior of the full-scale RC portal frames with EDH infilled wall system $(F_{I - EDH})$ and conventional stiffened (brick; CB) infilled wall system ( $F_{I - CB}$ ) are evaluated under cyclic loading and compared with that of the bare RC frame ( $F_{Bare}$ ).

Design of RC portal frame

Three full-scale models of single story single bay frames of dimension 3.0 m × 3.0 m are cast in the large-scale structural test facility at Indian Institute of Technology (IIT) Roorkee. The frame is designed as per Indian Standard IS 1893 (Bureau of Indian Standards (BIS), 2016b) and Indian Standard IS 13920 (BIS, 2016a) conforming to most severe seismic zone (V) of India. The concept of “Strong column–Weak beam” design philosophy is adopted to finalize the sectional details and reinforcement requirements of beams and columns of the frame. The inner dimensions of the frame are so proportioned that the aspect ratio of infill wall is unity. Moreover, the clear span of the beam and columns accommodates 10 units of slotted concrete blocks along the length and around 20 units along the height. The dimensions of the RC portal frame with the reinforcement details is shown in Figure 2.

A provision for a continuous groove at the center of the beam, column, and foundation is kept in the form-work of portal frames to facilitate the linking of the slotted blocks with the RC frame through rigid links. The sectional dimension of the continuous groove in column and foundation is 25 mm × 40 mm while it is 25 mm × 25 mm in beam. The clear cover of the columns and the foundation is kept as 50 mm while in the beam it is 30 mm to accommodate the grooves. The average compressive strength of the concrete calculated from cylinder specimens comes out to be 26.2 MPa with a coefficient of variation (COV) of 14.2%, 25.4 MPa with a COV of 13.7%, and 25.9 MPa with a COV of 16.8% (American Society for Testing and Materials (ASTM), 2005) for $F_{Bare}$ , $F_{I - EDH}$ , and $F_{I - CB}$ , respectively. Fe500 reinforcement bars are used in the construction of the frame. In the case of the brick infilled frame, bricks of size 230 mm × 110 mm × 70 mm with 1: 3 cement–sand mortar and an average compressive strength of brick prism as 7.3 MPa with a COV of 8.2% as per Indian Standard IS 1905 (BIS, 1987), mortar as 12.3 MPa with a COV of 7.4% and brick as 16.6 MPa with a COV of 10.6% as per Indian Standard IS 3495 (BIS, 1992). Running bond is maintained in the construction of the EDH infill wall and the average compressive strength of the concrete blocks comes out to be 29.8 MPa with a COV of 8.1%.

Construction of EDH infill wall system

The EDH infill wall is constructed with two main components: (a) slotted concrete blocks and (b) interlinking EDLs. Two types of slotted concrete blocks are used in the construction of the EDH infill wall: stretcher block and half block (Goyal and Agarwal, 2017). The dimension of the stretcher block is 300 mm × 230 mm × 150 mm and the half block is 150 mm × 230 mm × 150 mm. The volume of one stretcher block replaces approximately six first-class bricks of size 230 mm × 110 mm × 70 mm. The half blocks are used to maintain the running bond in the infill wall and are generally placed at either ends. A total of six slots, two each on the upper and on the lower faces and one each on both the side faces of the block are provided. The volume of the slots in the blocks is kept lower than 5% of the total volume of the block such that its strength and integrity remain unaffected under compression and crushing. The dimensions of the slots are calculated in such a way that the bearing failure of the blocks does not occur due to stress concentration around the links. The dimensional details of the stretcher and half block along with slot arrangement are given in Figure 3.

Two kinds of EDLs namely vertical and horizontal (Figure 4a and b, respectively) are used to interlink the slotted concrete blocks and finally construct the EDH infill wall system.

Vertical links are placed at both the top and the bottom slots of the block and horizontal links are placed in each side slot of the block. In the EDH infill wall, initially no mortar is used between the blocks; the links are the only restraining mechanism that keeps the blocks in position. Pointing of the blocks with low-strength mortar needs to be done after the construction of the infill to ensure water tightness and protection from other environmental factors. However, in this study, pointing is avoided to ensure reusability of the blocks after testing.

The rigid links are used to connect the blocks along the interface of the entire EDH infill wall and the RC frame with grooves along the center line. Apart from functioning as link between the infills and the frame, the role of the rigid links is to transfer the lateral forces from the frame to the EDH infill wall. Furthermore, the length of the rigid link varies depending on the space left between the blocks and the frame on the sides or top of the blocks of the EDH infill wall. The complete details of preparation of EDLs and rigid links and its connections (a) within EDH infill wall and (b) with EDH infill wall to RC frame through rigid links are explained as follows:

Preparation of EDLs and rigid links

The EDLs are prepared by using “ply” part (from jointless cap plies to the inner liner) of used radial rubber tires, which is a product of co-polymer of Styrene–butadiene rubber, Figure 4c and d. This “ply” of radial rubber tire contains steel wires (cords) embedded diagonally into it and is about 6 to 8 mm thick. Three or four pieces of “ply” are combined and sandwiched by steel plates of 0.5 mm thickness with the help of a high-strength adhesive under normal to high pressure. Steel plates on both sides of the links are provided for the enhancement of initial rigidity of the EDLs as well as to provide enough stiffness for the first yielding under lateral forces such as wind or minor tremor. Moreover, the thickness of the steel plate is kept minimum to facilitate early shear yielding of the links under large earthquakes. The role of the EDLs is manifold, namely (a) reduction of the stiffening effect of the infill wall as seen in the case of conventional infill; (b) dissipation of energy through yielding, which occurs due to the straining of the links and friction during the sliding motion of the blocks; and (c) regaining the original position of the wall due to its elastomeric properties, that is, the blocks retain their original position after dissipating the incipient energy. These links remain idle under gravity load and become active in the case of lateral loading and dissipate the incipient energy induced in the structure. Rigid links are made up of square pipes of mild steel with sectional dimensions similar to that of the slots of the concrete blocks and the grooves in the RC frame.

Connection details of the EDH infill wall with RC frame

The performance of the EDH infilled frame depends on four types of connections, namely (a) between block to block with the help of EDLs in the EDH infill wall, (b) between the bottommost row of the EDH infill wall with the foundation, (c) between the columns of the frame and the blocks at the ends of the EDH infill wall, and (d) between the topmost block row of the EDH infill wall with the beam.

The connection between blocks is made with the help of vertical and horizontal EDLs. The vertical links connect block rows along the bed joints and the horizontal links connect the blocks along the head joints as given in Figure 5 (Detail A). The orientation of every alternate vertical link is rotated orthogonally to consider the directional effects of earthquakes. Under lateral loading, the EDLs play a vital role in the energy dissipation mechanism, simultaneously maintaining the integrity of the infills even at large deformation.

The typical detail of the connection between the foundation and the bottommost row of the EDH infill wall is illustrated in Figure 5 (Detail D to F). The foundation is connected with the blocks at the bottommost row of the EDH infill wall. An arrangement is made in the foundation (or plinth beam) by providing a groove along its entire length in which a mild steel pipe of section 25 mm × 25 mm is inserted. Vertical rigid links of size 65 mm × 25 mm × 25 mm are welded on the inserted pipe at a spacing corresponding to that of the slots of the blocks of the lowermost row. The blocks are placed on the corresponding rigid links to form the bottommost connection. Furthermore, these links also account for the variation of the gap between different frame sizes and the blocks; since the rigid links of any size can be made at the site as per requirement.

The horizontal rigid links are inserted between the slots of the blocks and grooves of the columns, Figure 5 (Detail B). The gaps between the column and the blocks are filled with rich cement–sand mortar after placing the rigid links of the required size. The nature of the connection detail of type (a) does not allow smooth placing of the last row of the blocks. If the blocks are first placed in the last row, the placement of the rigid links connecting the beam becomes difficult. To overcome this, a connection between beam and the topmost block row of the EDH infill wall is developed as given in Figure 5 (Detail C). In this connection, vertical rigid links are placed directly connecting the penultimate layer of the block with the groove in the beam of the frame. The gap between the beam of the frame and the topmost block layer is filled with concrete to provide sufficient strength and confinement to the EDH infill wall.

Cyclic testing of RC frames with the EDH infill wall system

All the three RC frame portals are tested in lateral direction under the action of vertical loads in displacement control with three servo-hydraulic actuators, Figure 6. The complete load-deformation (hysteresis) behavior is obtained to evaluate the elastic and inelastic performance of each frame and its failure mechanism. Lateral displacement is applied through an actuator with 500 kN rated capacity and a stroke length of ±250 mm connected at the top of the frame through a loading beam. Two actuators of 250 kN rated capacity with a stroke length of ±250 mm are mounted vertically and connected with the same loading beam to apply a constant vertical load. Displacement-controlled sinusoidal cycles of increasing amplitude are applied on the top of the frame. The frame is tested with two cycles for each amplitude, with an increment of 5 mm up to 20 mm followed by 10 mm increments till the end of the test. The cycles are applied until there is a reduction in strength of the frame by 20% of its peak strength. The complete loading history protocol is followed as per FEMA 461 (Federal Emergency Management Agency (FEMA), 2007), Figure 6. The magnitude of vertical load is kept as 70.0 kN and is applied as two-point loading on the top of the beam such that the deflection profile of the beam of the portal frame is nearly similar to that under uniformly distributed load. The loading beam is connected with the frame through a special arrangement mounted at the exterior face of the beam–column joint of the frame and connected through an arrangement as illustrated in Figure 6 (Detail A). Special arrangements in the form of roller-bearing supports are also made to restrict the out-of-plane movement of the frame and to confine its deformation in the direction of in-plane loading, as given in Figure 6 (Detail B).

Analysis of the results

Initially all the RC frames behave elastically, $F_{Bare}$ and $F_{I - EDH}$ remain elastic until the end of 20 mm cycle while $F_{I - CB}$ shows elastic response until 15 mm. The flexural cracking of $F_{Bare}$ and $F_{I - EDH}$ starts at the cycle of 30 mm, while $F_{I - CB}$ shows flexural cracks on the columns as early as 20 mm. Beam plasticity is observed in the cycle followed by cracks forming at the beam–column interface and moving at 45 degrees toward the top of the beam. This phase is observed at a displacement of 40 mm in $F_{Bare}$ and $F_{I - EDH}$ and at 30 mm in $F_{I - CB}$ . The 50 mm cycle marks the development of prominent shear cracks on the columns in $F_{I - CB}$ along its height particularly at the regions of sliding cracks developed in the infill. Such shear cracks are not observed in $F_{Bare}$ and $F_{I - EDH}$ . Meanwhile, some flexural cracks are observed above the previously formed cracks at the base of the column in all the frames at this stage. This is followed by crushing and spalling of concrete at 120 mm in $F_{I - CB}$ and 130 mm in $F_{Bare}$ and $F_{I - EDH}$ . At 140 mm, there is a major loss of strength in the frame in $F_{I - CB}$ along with corner crushing of infills. The overall response of $F_{Bare}$ and $F_{I - EDH}$ is very similar, while $F_{I - CB}$ shows early development of all major distresses. However, the major distinction is the development of significant shear cracks in $F_{I - CB}$ , which is not prominent in $F_{Bare}$ and $F_{I - EDH}$ . The final crack pattern of $F_{Bare}$ , $F_{I - CB}$ , and $F_{I - EDH}$ after the tests and the corresponding hysteresis curves are shown in Figure 7.

In $F_{I - EDH}$ , the EDH infill wall system remains integrated with the portal frame during the initial stages of the test. The frame deforms in flexure, as in the case of $F_{Bare}$ , while the concrete blocks of the EDH infill wall slides one over the other, which initiates the process of dissipation of energy through friction between the blocks and by the straining of the EDLs. In $F_{I - CB}$ , the frame and the wall act in a fully composite manner up to a displacement of 15 mm. The following cycle of 20 mm is marked by the initiation of diagonal cracks in infills and a diagonal strut is developed, which increases the lateral stiffness of the frame. During 50 mm cycle, $F_{I - EDH}$ shows minor inelasticity in the infill with some crushing of the cement filling and the separation of the EDH infill from the frame while the development of the plastic hinge in the frame is similar to $F_{Bare}$ . In $F_{I - CB}$ , the diagonal cracks at the center of the wall on both sides are joined through horizontal sliding cracks at the mid height to form diagonal-sliding cracks as suggested by Mehrabi et al. (1996). During the 50 mm cycle to 70 mm cycle, $F_{I - CB}$ attains the peak strength owing to the formation and stiffening effect of the diagonal strut. At the same time, some minor cracks are formed in the blocks of the $F_{I - EDH}$ . However, the strength of the infilled frame increases due to the contribution of the EDH infill increasing with each cycle even after the hinging of the RC frame.

A major change occurs with the formation of two new rocking planes during the cycles of 110 and 130 mm accompanied by the spalling of concrete at the left corner below the beam–column junction in $F_{I - EDH}$ that meet at the center of the EDH infill wall, Figure 7e. The overall performance of the EDH wall is stable even up to 180 mm test cycle. Conversely, in $F_{I - CB}$ , during cycles of the 110–140 mm, the crushing of the infills is initiated at the center and at the corners. At the cycle of 140 mm, the infill gets fully disintegrated and the stiffening effect of the infill is completely lost. The test is stopped at the cycle of 160 mm after severe crushing of the infill, which occurs at the bottom corners and central regions along with spalling of mortar in the infill and concrete at the hinge regions.

Comparative assessment of EDH and conventional infill frame system

The peak lateral resistance of $F_{I - CB}$ and $F_{I - EDH}$ is 2.62 and 2.02 times higher than that of $F_{Bare}$ as given in Figure 8a. The post-yield behavior of $F_{I - EDH}$ is nearly constant even at the displacement cycle of 180 mm (drift of 6%). It is able to sustain the vertical and lateral load after the formation of plastic hinges in the frame that now act as a bounding element for the EDH infill wall. On the contrary, the post-yield behavior of $F_{I - CB}$ reduces significantly with the increase of the displacement cycle. At the deformation cycle of 160 mm (drift of 5.3%), the lateral resistance of $F_{I - CB}$ nearly reduces to half of the peak lateral load capacity and the infill wall is not able to take any further load and a mechanism develops in the frame that leads to its complete collapse. Similar observations are also reported in the past (Basha and Kaushik, 2016). At the cycle of 160 mm, $F_{I - EDH}$ shows residual resistance capacity of around 85% of its peak strength as shown in Figure 8a. The post-peak strength variation is also stable and sustainable in the case of $F_{I - EDH}$ in relation to both $F_{I - CB}$ and $F_{Bare}$ . The initial lateral stiffness of $F_{I - EDH}$ and $F_{I - CB}$ is nearly 1.54 times and 2.54 times of $F_{Bare}$ despite the compressive strength of the brick prism used in the CB infill is only 7.3 MPa, while the block compressive strength of EDH infill is 29.8 MPa. Furthermore, the strength and stiffness ratios of the CB infills alone to the bare frame are 1.49 and 1.61, respectively, and that of the EDH infills alone to the bare frame are 0.77 and 0.59, respectively. The strength and stiffness ratios of the CB infills with respect to the EDH infills are 1.93 and 2.72, respectively. The brick infill wall acts as a diagonal strut at low deformations and leads to an increase in stiffness; this phenomenon increases with the increase of unit (brick) strength.

The peak lateral load resistance capacity of both the infilled frame relative to bare frame is shown in Figure 8b. The lateral strength of $F_{I - EDH}$ is nearly two times than that of $F_{Bare}$ and there is no significant change as the imposed cyclic lateral deformation increases even up to 6% lateral drift. In the case of $F_{I - CB}$ , at the initial stages, the peak lateral strength is 3.12, but it decreases to 1.86 at a lateral drift of 5.3% similar to the values reported by Dautaj et al. (2018). There is only 6% decrease in the strength of $F_{I - EDH}$ , while $F_{I - CB}$ manifests 40% decrease in strength even at a lower drift. It means that the brick infill acts as diagonal strut and is responsible for the shear failure of the columns of the frame and also is not able to support the frame at large displacements. On the contrary, in $F_{I - EDH}$ , there is no diagonal strut behavior and the plastic hinges form in the frame very much similar to that of $F_{Bare}$ . It not only supports the frame but also resists the lateral and vertical load even at a lateral drift of 6%. This property of the EDH infill wall with RC frames develops a secondary load-resisting system in the frame and proves to be a better performing infill in the case of severe earthquakes. Figure 8b manifests that the stiffening effect of the CB infill wall system reaches its peak at a story drift of about 0.3%, which may be responsible for altering the load path afterwards with a sharp reduction and becomes nearly constant beyond the story drift of 2% with no contribution in load-resisting mechanism. In the case of the EDH infill wall system, the trend is nearly reverse, that is, there is neither sharp increase nor decrease in either lateral strength or stiffness. Figure 9a shows completely damaged infills of $F_{I - CB}$ after 160 mm with no resistance in both vertical and lateral direction, while Figure 9b shows the damaged state of $F_{I - EDH}$ after 180 mm cycle and shows that the EDH infill is still able to resist both lateral and vertical loads.

The energy dissipation capacity of both the infilled frames is much higher than the bare frame as expected, Figure 10a. The energy imparted in the structure is released or dissipated by the formation of plastic hinges in the region of maximum moment in the case of bare frame, which are responsible for the development of a mechanism that results in final collapse. In the case of the conventional infill frame, the energy is released or dissipated not only through the formation of plastic hinges in the frame but also through the cracking of the brick infill wall system. The difference in both the frame failure mechanisms is that in the case of the bare frame, flexure plastic hinges are formed; while in the case of the conventional infill wall frame system, the shear plastic hinges develop and fail in brittle or shear mode (Fiore et al., 2016). However, in the case of the EDH infill frame, a clear enhancement in the quality of energy dissipated is observed as the imparted energy dissipates through a number of sources, namely (a) through the formation of moment plastic hinges in the frame, (b) through the yielding of the EDLs, and (c) through friction between the block layers. Furthermore, a major contribution in the energy dissipation is through the inelastic activity in (b) and (c). Moreover, the EDH infill wall contributes to load-resisting mechanism within the hinged frame.

The effective damping, $ξ_{eff}$ , of the tested frames is calculated as per $ξ_{eff} = \frac{W_{D}}{4 π W_{s}}$ , where $W_{D}$ is the energy dissipated in a cycle and $W_{s}$ is the strain energy at the corresponding maximum displacement and are shown in Figure 10b. It increases with the increase in imposed cyclic deformation particularly in the case of $F_{Bare}$ and $F_{I - EDH}$ . However, in the case of $F_{I - CB}$ , it manifests a different phenomenon, that is, a decrease in the damping values in the earlier cyclic deformation during the formation of the diagonal strut and an increase in the damping values after the failure of the strut at a drift of 2%, which is similar to that recorded in the study by Morandi et al. (2018). The effective damping of $F_{I - EDH}$ varies from 10% to 17%; whereas in the case of $F_{I - CB}$ , it falls from 15% to 7% initially and later rises to 17%. $F_{I - EDH}$ with the links and friction augments the damping properties of the frame almost linearly up to a drift of 6%.

Development of numerical model of the EDH infill wall

The conceptualization and design of the EDH infill owes its origin to the efficient lateral performance of the high damping rubber (HDR) bearings. The advantages of the HDR bearings are utilized to enhance the performance of the infilled frames. The mechanical properties of the rubber used in EDLs are similar to that of the HDR bearings and their load deformation behavior is similar to the models developed by various researchers in the past (Kikuchi and Aiken, 1997; Koh and Kelly, 1988; Yamamoto et al., 2012; Yoshida et al., 2004). Even though the HDR models can accurately reproduce the lateral load deformation behavior of the EDLs, the numerical modeling of the EDH under the action of vertical load becomes more complex due to the additional frictional restoring forces generated in the system. Therefore, a modified numerical model is developed for capturing the complete behavior of the EDH infill wall under vertical and lateral loading.

Design of the test schedule

The aim of the test schedule is to develop a complete numerical model for the EDH infill by generating a model for the EDH unit ( $ED H_{u})$ . The test schedule is formulated taking into account the role of the $ED H_{u}$ in the lateral behavior of the infilled RC frames that paves the way for defining the behavior of the EDH infill as a whole. Even though the $ED H_{u}$ is repeated throughout the infill, its lateral behavior is not the same for each block since there is a variation in vertical forces between the block layers. Hence, decoupling of the constituent force mechanisms is essential due to the complexity of the problem caused by the variation of the vertical forces. Tests are conducted by varying the magnitude of the vertical forces on the $ED H_{u}$ . A pre-compression vertical force of 70.0 kN is applied on the top of the EDH infilled frame, $F_{I - EDH}$ , before the commencement of the test. A uniform distribution of the vertical load among the blocks that constitute one layer of the infill is assumed. The block at the bottom of the EDH infill experiences more force due to the cumulative effect of the mass of the blocks on top of it. A variation of the vertical forces from 0 kN to 27 kN, which is nearly thrice the average value of load experienced by the blocks, is assumed for the tests. The detail of a typical $ED H_{u}$ is given in Figure 11c. A system of blocks without links named block friction unit ( $B F_{u}$ ; Figure 11d) is tested under the same set of vertical loads to find the effect of friction on the blocks and to determine the coefficient of friction between the blocks. The quantification of the lateral behavior of the $ED H_{u}$ and $B F_{u}$ under varying amount of vertical forces gives necessary and sufficient information for the complete modeling of the EDH infill. The schedule of the tests is given in Table 1.

Table 1.

Test schedule for $ED H_{u}$ and $B F_{u}$

$ED H_{u}$ specimen		$B F_{u}$ specimen		Vertical pre-compression load (kN)
Serial No.	Name	Serial No.	Name
1	$ED H_{u 0}$			0
2	$ED H_{u 1}$	8	$B F_{u 1}$	1
3	$ED H_{u 4}$	9	$B F_{u 4}$	4
4	$ED H_{u 8}$	10	$B F_{u 8}$	8
5	$ED H_{u 12}$	11	$B F_{u 12}$	12
6	$ED H_{u 18}$	12	$B F_{u 18}$	18
7	$ED H_{u 27}$	13	$B F_{u 27}$	27

Test setup and instrumentation

The test specimen consists of three blocks placed one over the other with vertical links placed in the slots of the blocks, Figure 11a. A servo-controlled hydraulic actuator of 100 kN rated capacity and ±150 mm stroke length is employed in applying the lateral load. A double-acting jack is attached to the specimen to apply vertical load on the blocks and its variation is measured. To simulate the conditions in the infilled frame and to facilitate smooth movement of the blocks, rollers are provided at the bottom interface between the blocks and the loading jack. The blocks are restricted in out-of-plane direction by using two rollers on both sides of the specimen. The arrangement is devised in such a manner that the topmost block remains stationary and the bottom two blocks slide over the bottom roller. Each specimen is subjected to loading history as per FEMA 461 (FEMA, 2007) as shown in Figure 11d. A pilot study is conducted to find the displacement at which the links shear off completely. The test result shows that the shearing of the EDLs occur at a lateral displacement of 50 to 55 mm. On this basis, the tests are restricted to a maximum displacement of 45 mm.

Analysis of the test results

The force deformation hysteretic behavior of an $ED H_{u 0}$ gives the response of $ED H_{u}$ without vertical load, Figure 12a. It is used as the control model for the calculation of the effect of friction under vertical loads acting on the $ED H_{u}$ . The hysteresis behavior of $ED H_{u}$ and $B F_{u}$ under varying vertical loads is shown in Figures 12 and 13. It is manifested that the lateral strength of each specimen increases with an increase in vertical load. Essentially, the modeling of the frictional forces arises from the test of $B F_{u}$ that paves the way for the modeling of the $ED H_{u}$ .

The links under no yield condition, that is, at the starting point, during test and after the completion of the test is shown in Figure 14. It is observed that the links retain their shape even after 45 mm displacement and the major shear deformation is limited only to the mild steel plates. The region of maximum shear damage is at the interface of the block layers as expected, which is marked in dotted ellipses. The EDLs remain intact and are not only able to sustain further load deformation but also hold the blocks in position.

The damage occurring in the EDH infills in the infilled frame corresponding to a displacement cycle of 180 mm (drift of 6%) causes about 9 mm displacement of each $ED H_{u}$ (assuming linear distribution of displacement along the height). The tests on $ED H_{u}$ show stable behavior up to a displacement of 45 mm. The damage that has occurred to the EDLs are shown in Figure 14, which is insignificant even under a drift of 6%, which is more than 5% drift limit specified in FEMA 273 (FEMA, 1997) under the Collapse Prevention Performance Level.

Modeling approach for the EDH infill wall

The backbone curves of the test series on $ED H_{u}$ are presented in Figure 15a. $ED H_{u 0}$ represents the EDL forces while $ED H_{u 1}$ to $ED H_{u 27}$ represent a function of EDLs and frictional forces. The decoupling of the lateral restoring force, that is, EDL forces and frictional forces is the primary step in the modeling process. It is carried out by subtracting the frictional force component (calculated as discussed in the forthcoming section on $B F_{u}$ ) from the backbone curves of the $ED H_{u}$ tests on models ranging from $ED H_{u 1}$ to $ED H_{u 27}$ . This response matches closely with the $ED H_{u 0}$ test results with a good accuracy as shown in Figure 15b. The accuracy of this step paves the way for the next step in which the constituent forces are separately modeled.

Modeling of EDH_u0

The development of an appropriate model to simulate the behavior of $ED H_{u 0}$ is pivotal for the development of a model of the $ED H_{u}$ . The model of $ED H_{u 0}$ is developed by following the procedure presented by Yamamoto et al. (2012). The response of $ED H_{u 0}$ in lateral direction is decomposed into two components by assuming that the restoring action in lateral direction is due to the action of one component, $F_{r}$ , acting in a direction toward the origin and other component, $F_{s}$ , in a direction nearly opposite to the direction of motion. The component $F_{r}$ behaves as an elastic component with linear behavior under low strains and nonlinear behavior under higher strains, while component $F_{s}$ represents an elastoplastic component and is responsible for the energy dissipation as shown in Figure 16. These force components are found out with respect to vectors $\bar{p}$ and $q$ , where $\bar{p}$ is a unit vector along $p$ . $p$ is defined along the trajectory of motion and $q$ is defined with respect to vector $p$ as per the differential equations developed by Özdemir (1976) as given below:

\overset{\cdot}{q} = | \overset{\cdot}{p} / α | {\bar{\overset{\cdot}{p}} - {| q |}^{n} \bar{q}}

(1a)

q (0) = p (0) = 0

(1b)

where $| p |$ and $\overset{\cdot}{p}$ represent the absolute value and the time derivative of the vector $p$ . Also, $α$ and n are parameters that define the yield displacement and the shape of the curve, respectively.

The restoring force $F_{EDL}$ is defined as the summation of two components $F_{r}$ and $F_{s}$ directed along $- \bar{p}$ and $- q$ , respectively by the following equation:

F'_{EDL} = [\begin{matrix} - \bar{p}' & - q' \end{matrix}] {\begin{matrix} F_{r} \\ F_{s} \end{matrix}}

(2)

where the prime represents transpose of the vector. The values of $F_{r}$ and $F_{s}$ are obtained by solving this system of equations. The properties of the rubber used in the $ED H_{u 0}$ are obtained in terms of shear stresses $τ_{r}$ and $τ_{s}$ , given by:

τ_{r} = F_{r} / A and τ_{s} = F_{s} / A

(3)

where A is the combined shear area of the links.

The model is established by using five parameters calculated by equating the force deformation response of the experimental data to the numerical model. Nonlinear least square method is used to find out the coefficients of the model. The stresses $τ_{r}$ and $τ_{s}$ are found out as:

τ_{r} = 0.022 γ for 0 \leq γ \leq 1.0

(4a)

τ_{r} = 0.022 γ + 1.764 {(γ - 1.0)}^{2} for γ > 1.0

(4b)

τ_{s} = 1.784 + 0.2 γ + 0.21 γ^{3}

(5)

where $γ$ is the absolute shear strain of the links with height $h$ given by:

γ = | p | / h

(6)

These equations can be effectively used to model the hysteretic behavior of the $ED H_{u 0}$ . Figure 17a and b show the load-deformation behavior for the experimental results and for the analytical model developed, respectively.

The model of $ED H_{u 0}$ is reproduced by using YamamotoBiaxialHDR element available in OpenSees software (Open System for Earthquake Engineering Simulation (OpenSees), 2013). This model is developed for capturing the bidirectional and unidirectional behavior of HDR bearings based on the properties of X0.6 Bridgestone rubber. A close match between the experimental results, Figure 17a, and the YamamotoBiaxialHDR element in OpenSees, Figure 17c, is obtained by calibrating the parameters of the model. The degree of match between the models is given as the comparison of the energy dissipated as shown in Figure 17d.

Modeling of BF_u

The study on $B F_{u}$ gives an insight into the behavior of the blocks under friction. Figure 18a shows the backbone curves of the hysteresis curves obtained from the tests on $B F_{u}$ . To effectively model the friction between the blocks, the coefficient of Coulomb friction between the blocks is measured. Figure 18b shows the variation of frictional forces with respect to the applied compressive preload calculated from the tests on $B F_{u}$ .

F_{f} = μ (P)

(7)

where $F_{f}$ is the frictional force, $μ$ is the coefficient of friction, and $P$ is the compressive preload applied. The coefficient of friction calculated gives an average value of 0.77 with a COV of 12.9%.

For the numerical modeling of the friction along the block interface, the SingleFPBearing element (Zayas et al., 1987) is utilized. This element is developed for single friction pendulum and is defined using three parameters including coefficient of friction, $μ$ , the initial stiffness, $k_{init}$ , and the effective radius of concave sliding surface, $R_{eff}$ . This model captures the frictional behavior of the $B F_{u}$ . Two typical test results for compressive preloads of 4 and 27 kN are showcased to validate the closeness of the model used to reproduce friction as shown in Figure 19.

Modeling of EDH_u

The numerical model is developed in OpenSees by combining the YamamotoBiaxialHDR element in parallel combination with SingleFPBearing element as shown in Figure 20a and the lateral resistance $F_{ED H_{u}}$ is calculated as per the following equation.

F_{ED H_{u}} = F_{EDL} + F_{f}

(8)

The combination of these elements in parallel reproduces the behavior of $ED H_{u}$ with a good amount of accuracy. The increase in the lateral strength of the $ED H_{u 1}$ to $ED H_{u 27}$ with the increase in vertical load is captured by this model. Also, the reloading of the frictional behavior of $B F_{u}$ is rapid with high unloading stiffness as the frictional restoring forces change direction abruptly with the reversal of direction of motion. However, with the presence of EDLs, the reloading becomes gradual due to the straining of the EDLs and the resistance it generates is captured by the model. This behavior is simulated through calibration of the model parameters. The values of the calibrated model parameters are given in Table 2. The comparison of the results of numerical and experimental tests of $ED H_{u 1}$ , $ED H_{u 8}$ , and $ED H_{u 18}$ are given in Figure 20.

Table 2.

Parameters of calibrated $ED H_{u}$ model

YamamotoBiaxialHDR			SingleFPBearing
$D D_{o}$ (m)	$D D_{i}$ (m)	$H_{r}$ (m)	$μ$	$k_{init}$ (N/m)	$R_{eff}$
0.2	0	0.0073	0.77	6.00E + 05	100

HDR: high damping rubber.

Table 3 shows the ratio of lateral resistance and energy dissipated by the experimental and numerical models for $B F_{u}$ and $ED H_{u}$ . The values are calculated at each displacement as the mean of the ratios for all the tests across the samples $B F_{u 1}$ to $B F_{u 27}$ . The COV, which shows the dispersion of the data is also reported. The same procedure is repeated for samples $ED H_{u 1}$ to $ED H_{u 27}$ . The mean of the ratios for $B F_{u}$ is 1.14 with a COV of 12.64% and 1.05 with a COV of 13.35% for lateral resistance and energy dissipation per cycle, respectively. The similar values for $ED H_{u}$ are 1.13 with a COV of 18.29% and 1.04 with a COV of 18.77%. The above ratios give an idea about the accuracy and the margin of error of the model developed and show that a reasonable accuracy between the models is achieved.

Table 3.

Ratio of lateral resistance and energy dissipated (experimental/numerical)

Displacement (mm)	$B F_{u}$				$ED H_{u}$
	Lateral resistance		Energy		Lateral resistance		Energy
	Mean	COV	Mean	COV	Mean	COV	Mean	COV
5	1.12	15.70	0.97	12.82	1.09	22.02	1.06	23.08
10	1.17	10.63	1.05	15.81	0.95	13.95	1.03	29.26
15	1.05	10.37	1.02	12.00	0.95	14.36	1.11	22.93
20	1.04	11.05	1.01	15.39	1.04	25.72	1.20	27.66
25	1.07	17.02	1.03	12.86	1.14	22.30	1.16	25.76
30	1.09	16.59	1.04	15.06	1.23	21.85	1.05	18.10
35	1.23	6.31	1.11	11.28	1.27	20.85	0.96	10.15
40	1.29	15.63	1.14	13.95	1.27	16.34	0.92	7.02
45	1.24	10.47	1.07	10.96	1.21	7.24	0.91	5.01
Mean	1.14	12.64	1.05	13.35	1.13	18.29	1.04	18.77

BF: block friction; EDH: energy dissipating hysteretic; COV: coefficient of variation.

Validation of the numerical model

The modeling of $F_{I - EDH}$ is carried out as the superposition of the model of $F_{Bare}$ and the EDH infills. The modeling of the $F_{Bare}$ is carried out in OpenSees using lumped plasticity model, which is defined by concentrating the nonlinearity of the member in hinges defined in its plastic hinge regions through force–deformation or moment–rotation relationship. The RC frame of the EDH infilled frame can be ideally modeled by using this method as the amount of shear damage of the frame members due to the addition of the infill is not prominent in the EDH infilled frame system. This is due to the absence of the formation of the diagonal strut in the EDH infilled frame. Also, the crack pattern in the RC frame of $F_{I - EDH}$ is similar to that observed in the $F_{Bare}$ (Figure 7). Thus, the approximation of the RC frame by lumped plasticity does not affect the accuracy of the modeling. In this study, the nonlinear response of the members is approximated using the Modified Ibarra–Medina–Krawinkler Deterioration Model with Peak-Oriented Hysteretic Response (ModIMKPeakOriented material; Ibarra et al., 2005; Ibarra and Krawinkler, 2005) available in OpenSees. The equations given by Haselton et al. (2008) are used to predict the parameters of the frame members. The coefficients of the ModIMKPeakOriented material are calibrated to give an optimized match between the experimental and numerical values. The model calibration of the numerical and the experimental results is performed by minimizing the error in the backbone curve and energy dissipated by the two models. The comparison of the hysteresis curves of $F_{Bare}$ are shown in Figure 22a.

The modeling of $F_{I - EDH}$ is carried out by placing $ED H_{u}$ elements at corresponding locations as they are placed in the experimental model. One element is used to model each $ED H_{u}$ in the infilled frame as shown in Figure 21. The infill modeling is affected by the distribution of the vertical forces coming into the $ED H_{u}$ which is considered in the modeling of the friction component of the $ED H_{u}$ . The vertical force on the topmost $ED H_{u}$ is 7.0 kN and that on the bottommost is 12.0 kN. The results of the infilled frame thus obtained are compared with the experimental results as shown in Figure 22b and show a good amount of accuracy. The ratio of response of the experimental and numerical models in terms of lateral resistance, energy dissipation, and effective damping along with mean and COV of the responses are furnished in Table 4. The numerical model of $F_{I - EDH}$ captures the experimental response with good accuracy.

Table 4.

Ratio of responses (experimental/numerical) of $F_{I - EDH}$

Displacement (mm)	Lateral resistance	Energy	Effective damping
40	1.11	1.31	1.23
80	1.22	1.00	0.73
120	0.98	0.91	0.98
160	0.96	1.14	1.17
180	0.91	1.13	1.13
Mean	1.03	1.01	0.96
COV	10.06	13.57	18.35

COV: coefficient of variation.

Conclusion

The EDH infill wall has two prominent sources of energy dissipation, namely friction and elastomeric damping. The friction comes into play between the sliding surface of one block over the other and its movement is restricted by the yielding of EDLs. The cyclic performance of EDH infilled frame system is compared with the CB infilled frame as well as the bare frame. The main conclusions of the study based on in-plane testing of the infilled frame are summarized as follows:

The EDH infill frame shows an improvement over the CB infill frame with the absence of the formation of the diagonal strut and the consequent reduction in the stiffening effect. This stiffening effect is directly proportional to the strength of the unit, mortar and other interaction parameters in the conventional infill frame. However, in the case of the EDH infill, a low stiffening effect is observed. This effect is nearly independent of the unit strength since it is a function of surface friction as well as yielding of the EDLs.

The EDH infill wall system helps in the dissipation of incipient energy imparted during severe earthquakes. At the same time, it acts as a secondary load-resisting system after the formation of plastic hinges in RC frames. The EDH infill wall may significantly reduce the possibility of collapse of a multi-storied RC building during severe earthquakes.

The stable and better post-peak behavior of the frame with EDH wall is a major achievement over the conventional infill frame that may lead to brittle failure of the structure. An increase in the post-peak stiffness in the case of the EDH infill frames is observed against the steep fall in the post-peak stiffness in the case of the conventional infill frame.

A numerical model for the energy-dissipating infill wall system is developed based on its constitutive components. Two sources of energy dissipation, namely friction damping mechanism between the blocks and the yielding of link elements are identified and separately modeled. The developed model is validated and calibrated using the cyclic test data with a good accuracy and it highlights the mechanism of lateral resistance of the energy-dissipating infill wall system.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Nidhin S Pachappoyil

Pankaj Agarwal

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Cyclic evaluation of energy-dissipating hysteretic infilled reinforced concrete frame: A novel approach as low-cost passive energy–dissipating device